Two rhombuses have sides with lengths of #4 #. If one rhombus has a corner with an angle of #(7pi)/12 # and the other has a corner with an angle of #(pi)/8 #, what is the difference between the areas of the rhombuses?

Question

Two rhombuses have sides with lengths of #4 #.  If one rhombus has a corner with an angle of #(7pi)/12  # and the other has a corner with an angle of #(pi)/8  #, what is the difference between the areas of the rhombuses?

Claire Akin · Accepted Answer

Difference in areas between the two rhombuses is 9.332

Area of rhombus #= (1/2) * d_1 * d_2 or a * h#
Where #d_1 , d_2 # are the diagonals, a is the side and h is the altitude.

In this case we will use the formula Area = a * h.

Carson Arnold · Answer

undefined To find the area of a rhombus, you can use the formula: Area = (diagonal1 * diagonal2) / 2. Since both rhombuses have sides of length 4, we can find their diagonals using trigonometry.

For the rhombus with an angle of (7π)/12, we can use the law of cosines to find one of its diagonals:
diagonal1 = √(4^2 + 4^2 - 2 * 4 * 4 * cos((7π)/12))

For the rhombus with an angle of (π)/8, we can similarly find one of its diagonals:
diagonal2 = √(4^2 + 4^2 - 2 * 4 * 4 * cos((π)/8))

Then, we can find the areas of both rhombuses using the formula mentioned earlier and find their difference.

After calculating the areas of both rhombuses and subtracting them, we find the difference between their areas.